Turbulent-like velocity fluctuations in two-dimensional granular materials subject to cyclic shear.

We perform a systematic experimental study to investigate the velocity fluctuations in the two-dimensional granular matter of low and high friction coefficients subjected to cyclic shear of a range of shear amplitudes, whose velocity fields are strikingly turbulent-like with vortices of different scales. The scaling behaviors of both the transverse velocity power spectra () ∝ and, more severely, the longitudinal velocity power spectra () ∝ are affected by the prominent peak centered around ≈ 2π of the inter-particle distance due to the static structure factor of the hard-particle nature in contrast to the real turbulence. To reduce the strong peak effect to the actual values of (the subscript '' refers to either T or L), we subsequently analyze the second-order velocity structure functions of (2)ν() in real space, which show the power-law scalings of (2)ν() ∝ for both modes. From the values of , we deduce the corresponding from the scaling relations of = + 2. The deduced values of increase continuously with the shear amplitude , showing no signature of yielding transition, and are slightly larger than = 2.0 at the limit of → 0, which corresponds to the elastic limit of the system, for all . The inter-particle friction coefficients show no significant effect on the turbulent-like velocity fluctuations. Our findings suggest that the turbulent-like collective particle motions are governed by both the elasticity and plasticity in cyclically sheared granular materials.